7 Discussion

The structure of interstellar clouds remains a subject of debate because different observations suggest different, and often contradictory, interpretations. The Thoraval et al. (1999) results, based on infrared observations are sensitive mainly to the dust distribution and thus probably to the bulk of the mass distribution. On the contrary, some low-abundance species (see for example Marscher et al. 1993 and Moore & Marscher 1995 results) exhibit large abundance variations down to the smallest accessible scales.

Our results show that the structuring of the gas by the turbulent velocity field leads naturally to different distributions for different species, without requiring any external mechanism. Thus, seemingly contradictory observations find a unified explanation which applies to any turbulent region in the interstellar medium. Naturally, this does not preclude a significant influence of other mechanisms. Star formation does occur within clouds and leads to a number of fancy phenomena that stimulate the imagination of the modelist. We still need to explain how turbulence survives and is fed despite its fast dissipation timescale. However, since it is there, it must be taken into account.

In this paper, we have shown how interstellar turbulence properties could be reduced to a small number of quantitative parameters by wavelet analysis. A pure log-normal cascade (as in incompressible turbulence) is characterised with only two numerical quantities. Deviation from that behaviour could be managed with a third. These parameters are directly accessible from observations, but require fully sampled, large-scale, high-resolution maps. New observational facilities such as array detectors now available at the 30 m IRAM observatory (HERA), or the future ALMA project should provide such maps at a reasonable cost.

Figure 16: Decimal logarithm of density as a function of scale.

These parameters can be used to build synthetic velocity fields at a numerical cost well below that of solving the full Navier-Stokes equations. Time and length scales are easily adjusted to the observations, allowing for direct comparison of predicted and observed structures. Generalisation to 2D and 3D fields of techniques described here is straightforward, but would then require the use of large, massively parallel computers. It is not obvious that qualitatively different results would result from such an extension, with one exception: a 1D velocity field precludes vorticity and so our density field probably has excessive contrasts when matter is squeezed between two cells with opposite velocity direction. Extension of the chemical set is straightforward.

We have shown that a density structure develops with different scale properties for different chemical species. The mixing properties of turbulence ensure that on any line of sight a fraction of the gas is in a far from equilibrium state. Thus species that do not peak at the same evolutionary stage in a classical time-dependent model can coexist naturally without the need to invoke any "early-stage'' argument. Conversely no indication about the age of the cloud may be derived from abundance ratios.

Acknowledgements

We thank J. Pety for providing centroids map of Polaris prior to publication (Pety & Falgarone submitted, Pety 1999), D. Pelat for many discussions on subtle statistical matters, A. Arnéodo for discussions during a one week post-graduate course in Bordeaux, and E. Falgarone and the referee for numerous useful comments.